Method for locating a connected object by phase differences of arrival in an LPWA network

ABSTRACT

A method for locating a connected object within an LPWA network using a plurality of base stations. The connected object transmits packets in RF frequency channels forming a virtual band being scanned once in the uplink direction and once in the downlink direction in a symmetrical manner. The base stations receiving the signal perform an RF to intermediate frequency translation and then a baseband translation in digital mode. The phase differences of arrival for each pair of base stations and the attenuation coefficients of each transmission channel between the connected object and each base station enable a composite transfer function to be constructed for each pair of base stations. The peaks of highest amplitude are detected in the corresponding impulse responses and the distance differences between the connected object and the different base stations are derived therefrom. The position of the object is then estimated by hyperbolic trilateration.

TECHNICAL FIELD

The present invention relates to the general field of locating objectsand in particular connected objects in a narrowband LPWA (Low Power WideArea) network such as a LoRa, SigFox or NB-IoT network.

STATE OF PRIOR ART

The geolocation of connected objects has become an important issue inthe field of IoT (Internet of Things). It allows especially to enrichinformation transmitted by these objects with locating information, tomanage the network more efficiently and develop geographical trackingapplications when the objects are mobile.

A first geolocation possibility consists in equipping connected objectswith GNSS (Global Navigation Satellite System) reception modules.However, this option is costly and is generally not compatible with thevery strict energy consumption requirements of these objects.Furthermore, it is excluded when connected objects are deployed in anindoor environment.

A second geolocation possibility is to perform trilateration from radiosignals transmitted by the connected objects and received by differentbase stations. However, the signals transmitted in LPWA networks,whether they use a licensed (NB-IoT) or unlicensed (SigFox, LoRa) band,are low rate and narrow band to propagate over long distances (up toseveral kilometres). The fact that the radio signals emitted arenarrowband leads to a significant inherent limitation in the time ofarrival (ToA) resolution of these signals and therefore to a lowdistance resolution of the position of the connected objects. This lowtime resolution can especially lead to large position errors when thetransmission channels are multipath, insofar as the different pathscannot be discriminated.

In the field of radar, it is known to measure a distance to a targetusing a plurality of narrow band signals, so as to avoid the need forhigh frequency ADC converters. More precisely, this technique (known asstepped frequency radar) consists in varying the carrier frequency ofthe transmitted signal by successive hops while maintaining aninstantaneous narrow band, the complex response being then measured foreach carrier frequency. By coherently combining the measurements, ormore precisely by performing an inverse Fourier transform of themeasurements obtained in this way, an impulse response of the channel inthe time domain is obtained. The temporal resolution is then inverselyproportional to the virtual frequency bandwidth scanned and no longerproportional to the instantaneous bandwidth. A similar technique, called“coherent multi-channel ranging”, has been applied in Low Rate WirelessPersonal Area Network (LR WPAN) networks to determine the position ofZigBee transponders, as described in the paper by M. Pichler et al.entitled “Multi-channel distance measurement with IEEE 802.15.4 (ZigBee)devices” published in IEEE Journal of selected topics in signalprocessing, Vol. 3, No. 5, October 2009, pp. 845-859. However, theaforesaid paper resorts to strong restrictive hypotheses on thepropagation scenario, namely a line-of-sight (LOS) situation and theabsence of multipath.

The previous technique was used to estimate the distance between aconnected object and a base station in an LPWA network and, bytrilateration using several base stations, to estimate the position ofthis object. This method, known as Phase of Flight (PoF) measurement,was described in the paper by F. Wolf et al. entitled “Coherentmulti-channel ranging for narrowband LPWAN: simulation andexperimentation results”, Proc. of 15th Workshop on Positioning,Navigation and Communication (WPNC), 2018, pp. 1-6. The advantage ofthis method lies in the fact that phase and frequency offsets betweenthe connected object and the different base stations can be dispensedwith by means of a round-trip transmission of a packet between theconnected object and each node. However, it assumes that the IoT networkallows such bi-directional transmissions and furthermore requires thetransmission of a large number of packets, a number that increases withthe number of base stations involved in locating. Furthermore, the riskof collisions between packets, especially if the network is dense, canlead to a significant degradation of network performance.

Another locating method that does not require synchronisation betweenthe node to be located and the base stations, while allowing reductionin the number of packets to be transmitted, has been described in patentapplication DE-A-10 2007 043 649. This method utilises hyperbolictrilateration based on the phase differences of arrival of a packettransmitted by the object to be located.

The principle of hyperbolic trilateration based on time of arrival (ToA)is illustrated in FIG. 1 .

A connected object, designated as WSN (Wireless Sensor Network) Node inFIG. 1 , is represented in 110 and LPWA base stations in 120. Thestations are assumed to be synchronised with each other by means of asame clock. The times of arrival of a packet transmitted by theconnected object and received by the base stations subtracted in two bytwo, in modules 130, the time difference of arrival for two basestations BS_(i) and BS_(l) corresponds to a propagation path difference:Δd _(il) =c _(light)(t _(i) ^(A) −t _(l) ^(A))  (1)

where c_(light) is the speed of light.

Assuming that the propagation paths between the connected node and thebase stations are in line of sight (LOS), the measurement of the timedifferences of arrival between at least 3 (resp. 4) base stationsenables the position of the object in the plane (resp. space) to bedetermined, by means of hyperbolic trilateration using the calculationmodule 140.

In practice, more time difference of arrival measurements are availablethan the minimum required, so that the system of equations isoverdetermined. Quadratic error minimisation techniques with thecalculation of a pseudo-inverse matrix are then used to solve the systemof equations.

The locating method by time differences of arrival requires the use ofbroadband signals (which are therefore well defined in time). Incontrast, since LPWA networks are narrowband, the virtual band techniquementioned above can be implemented by coherently combining phasedifference of arrival measurements between base stations at a pluralityof frequencies. In this case, the modules 130 perform a correlation ofthe signals received at the different frequencies and then an IDFT onthe results thus obtained at the different frequencies, before solvingthe aforesaid system of equations in the calculation module 140.

However, this latter approach requires a reference node (geolocatedobject) transmitting signals allowing the base stations to synchroniseand phase-match each other. However, the addition of such a referencenode, moreover located at the intersection of coverage zones of thevarious base stations participating in locating, does not lend itselfwell to the context of an LPWA network, especially when it is deployedin an outdoor environment. This synchronisation with the reference noderequires additional packets to be transmitted/received, which weighsupon the network load and increases consumption of the base stations.Furthermore, the transmission of the reference node should besynchronous with the node to be located, which is in contradiction withthe asynchronous nature of the LPWA network.

It is therefore an object of the present invention to provide a methodof accurately locating a connected object in an LPWA network that doesnot require a large number of packets to be transmitted nor does itrequire accurate synchronisation of base stations by means of areference node.

DISCLOSURE OF THE INVENTION

The present invention is defined by a method for locating a connectedobject in an LPWA network using a plurality of base stations, theconnected object transmitting an RF signal comprised of a sequence ofpackets in a plurality of frequency channels forming a virtual band, thevirtual band being scanned a first time according to a first channelsequence and a second time according to a second channel sequence, thefirst and second channel sequences being time symmetrical, said locatingmethod being specific in that:

(a) each base station performs translation of the RF signal at thechannel frequency, sampling of the RF signal translated, and thenbaseband translation in digital mode by multiplication with phasors, thesampling being synchronous with a general clock, common to all the basestations;

(b) each base station estimates the attenuation coefficient of thetransmission channel between the connected object and itself, inbaseband, as well as a phase of arrival of a packet, called a phase ofarrival, for each frequency channel of the first and second channelsequences;

(c) each base station sums the phases of arrival of packets relating toa same channel but to distinct channel sequences to obtain an averagedphase of arrival for each channel (Φ_(c) ^([T,R) ^(i) ^(]));

(d) each base station estimates the frequency offset ({circumflex over(δ)}_(f) ^([R) ^(i) ^(])) between its sampling frequency and that of thetransmitter, and then corrects the averaged phase of arrival for eachchannel of a phase error due to this frequency offset, so as to obtainan averaged and corrected phase of arrival (Φ′_(c) ^([T,R) ^(i) ^(]));

(e) each base station transmits the previously estimated attenuationcoefficients and averaged and corrected phases of arrival to a server;

(f) the server calculates, for each pair of base stations of saidplurality, the averaged and corrected phase differences of arrival so asto obtain phase differences of arrival ({Φ_(c) ^([R) ^(i) ^(,R) ^(l)^(])=Φ_(c) ^([T,R) ^(i) ^(]))−Φ_(c) ^([T,R) ^(i) ^(]))}), for eachchannel frequency;

(g) the server constructs, for each pair (BS_(i),BS_(l)) consisting of afirst and a second base station, a composite transfer function ({tildeover (H)}^([R) ^(i) ^(,R) ^(l) ^(])) relating to these two basestations, from the attenuation coefficients of the transmission channelbetween the connected object and the first base station (respectivelythe second base station) for the different frequency channels, as wellas the phase differences of arrival obtained in the previous step forthe said pair of base stations and for these same frequency channels;

(h) the server performs an inverse Fourier transform of each compositetransfer function obtained in the previous step so as to obtain acomposite impulse response) for each pair of base stations of saidplurality;

(i) the server detects the peak of highest amplitude in each of thecomposite impulse responses and derives therefrom, for each pair(BS_(i),BS_(l)) consisting of a first and a second base station, adistance difference (Δd_(il)) between the connected object and the firstbase station, on the one hand, and between the connected object and thesecond base station, on the other hand;

(j) the server estimates the position of the connected object byhyperbolic trilateration from the distance differences obtained in theprevious step.

Advantageously, the first channel sequence is obtained by scanning inthe uplink direction and the second channel sequence is obtained byscanning in the downlink direction, the uplink and downlink scans beingperformed uniformly with a constant frequency hopping (Δf).

Preferably, in step (a), the baseband translation is performed bymultiplying, at the sampling frequency rate, the samples of the RFsignal translated, by phasors exp(−j2πf_(c)kT_(s)) where f_(c) is thechannel frequency, f_(s)=1/T_(s) is the receiver sampling frequency andk is the sample rank.

According to a preferred alternative, in step (b), estimating thetransmission channel coefficient and the phase of arrival of a samplepacket is achieved by correlating the sequence of the baseband signalsamples with a pilot sequence, the modulus of the correlation resultbeing comprised of the transmitter and receiver gains to obtain saidtransmission channel coefficient.

Likewise, in step (c), the base station can perform, for each frequencychannel, the sum of Φ_(c) ^([T,R) ^(i) ^(])=ϕ_(c) ^([T,R) ^(i)^(])+ϕ_(2C+1−c) ^([T,R) ^(i) ^(]), ϕ[^(T,R) ^(i) ^(]) being the phase ofarrival of the packet c transmitted at the channel frequency f_(c) in afirst scanning direction and ϕ_(2C+1−c) ^([T,R) ^(i) ^(]) is the phaseof arrival of the packet 2C+1−c transmitted at the channel frequencyf_(c), in a second scanning direction opposite to the first one, K isthe number of samples in a packet and C is the number of packets perscanning direction.

In step (d) the averaged phase of arrival Φ_(c) ^([T,R) ^(i) ^(]) can becorrected by

$\Phi_{c}^{\prime^{\lbrack{T,R_{i}}\rbrack}} = {\Phi_{c}^{\lbrack{T,R_{i}}\rbrack} + {4{\pi\left( \frac{{\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}}{1 + {\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}} \right)}f_{c}{CKT}_{s}}}$where δ_(f) ^([T,R) ^(i) ^(]) is the frequency offset estimated in thesame step, f_(c) is the channel frequency, C is the number of packetsper scan, K is the number of samples per packet and f_(s)=1/T_(s) is thesampling frequency.

In any case, in step (g), for each pair of base stations consisting of afirst base station BS_(i) and a second base station BS_(l), the serverconstructs the composite transfer function by {tilde over (H)}_(c) ^([R)^(i) ^(,R) ^(l) ^(])=α_(c) ^([T,R) ^(i) ^(])α_(2C+1−c) ^([T,R) ^(i)^(])α_(c) ^([T,R) ^(l) ^(])α_(2C+1−c) ^([T,R) ^(l) ^(]) exp(jΦ^([R) ^(i)^(,R) ^(l) ^(])) where α_(c) ^([T,R) ^(i) ^(]), α_(2C+1−c) ^([T,R) ^(i)^(]) are the attenuation coefficients of the transmission channelbetween the connected object and the base station BS_(i) at the channelfrequency f_(c), respectively in the first and second scan, where α_(c)^([T,R) ^(l) ^(]), α_(2C+1−c) ^([T,R) ^(l) ^(]) are the attenuationcoefficients of the transmission channel between the connected objectand the base station BS_(i) at the channel frequency f_(c), respectivelyin the first and second scan, and where Φ_(c) ^([R) ^(i) ^(,R) ^(l) ^(])is the phase difference of arrival obtained in step (f) for the basestation pair BS_(i),BS_(l), and for the channel frequency f_(c).

In step (i), the distance difference between the connected object and afirst base station BS_(i) on the one hand, and the connected object anda second base station BS_(l) on the other hand is typically obtained by

${\Delta\; d_{i\;\ell}} = {\frac{c_{light}}{2}\underset{t}{\arg\mspace{14mu}\max}\left( {{{\overset{\sim}{h}}^{\lbrack{R_{i},R_{\ell}}\rbrack}(t)}} \right)}$where {tilde over (h)}^([R) ^(i) ^(,R) ^(l) ^(])(t) is the compositeimpulse response obtained in step (h) for the pair of base stationsBS_(i), BS_(l), and c_(light) is the speed of light.

The overall clock may be given by a GNSS receiver module equipping eachof the base stations of said plurality.

Alternatively, the overall clock can be obtained via the Internet usingthe NTP protocol from a time server.

Further alternatively, the overall clock may be obtained via a backhaulnetwork of a 5G network.

A second embodiment of the invention further relates to a method forlocating a connected object in an LPWA network using a plurality of basestations, the connected object transmitting an RF signal consisting of asequence of packets in a plurality of frequency channels forming avirtual band, the virtual band being scanned a first time, in accordancewith a first channel sequence and a second time in accordance with asecond channel sequence, the first and second channel sequences beingtime symmetrical, said method being specific in that:

(a) each base station performs translation of the RF signal at thechannel frequency, sampling of the RF signal translated, and thenbaseband translation in digital mode by multiplication with phasors, thesampling being synchronous with a general clock, common to all the basestations;

(b) each base station estimates the attenuation coefficient of thetransmission channel between the connected object and itself, inbaseband, as well as a phase of arrival of a packet, called a phase ofarrival, for each frequency channel of the first and second channelsequences;

(c) each base station sums the phases of arrival of packets relating toa same channel but to distinct channel sequences to obtain an averagedphase of arrival for each channel (Φ_(c) ^([T,R) ^(i) ^(]));

(d) each base station estimates the frequency offset ({circumflex over(δ)}_(f) ^([R) ^(i) ^(])) between its sampling frequency and that of thetransmitter, and then corrects the averaged phase of arrival for eachchannel by a phase error due to this frequency offset, so as to obtainan averaged and corrected phase of arrival (Φ′_(c) ^([T,R) ^(i) ^(]));

(e) each base station transmits the previously estimated attenuationcoefficients and averaged and corrected phases of arrival to a server;

(f) the server comprises a previously trained neural network, theattenuation coefficients and the averaged and corrected phases ofarrival for each base station of said plurality being provided to theinput layer of the neural network and the output layer of the neuralnetwork providing an estimate of the position of the connected object.

BRIEF DESCRIPTION OF THE FIGURES

Further features and advantages of the invention will become apparentfrom a preferred embodiment of the invention, described with referenceto the accompanying figures among which:

FIG. 1 , already described, schematically represents the principle of ahyperbolic trilateration locating in an LPWA network, known from thestate of the art;

FIG. 2 schematically represents the architecture of a receiver in a basestation of an LPWA network participating in the implementation of theinvention;

FIG. 3 schematically represents a virtual band scan that can be used inthe locating method according to one embodiment of the invention;

FIG. 4 represents the flowchart of a method for locating a connectedobject in an LPWA network according to a first embodiment of the presentinvention;

FIG. 5 schematically represents a method for locating a connected objectaccording to a second embodiment of the invention;

FIG. 6 illustrates in an example the performance of a method forlocating a connected object according to the invention in comparisonwith that of a locating method known from the state of the art.

DESCRIPTION OF THE EMBODIMENTS

In the following, an LPWA (Low Power Wide Area) network as set forth inthe introductory part will be considered, for example a LoRa, SigFox orNB-IoT network. These networks are especially characterised by the useof narrow band signals (typically from a hundred Hz to a hundred kHz)and low data rate to allow long range communications (typically from onekm to a few tens of km).

The nodes of an LPWA network include, on the one hand, connectedobjects, also called terminal nodes, and, on the other hand, basestations. A connected object served by a base station exchanges datapackets with it over a transmission channel which is generally of themultipath type.

In the following, the signal transmitted by the transmitter of aconnected object and received by a base station of the LPWA network willbe considered. Values relating to the transmitter (that is the connectedobject) are conventionally designated by the subscript T and thoserelating to the receiver (that is a base station) by the subscript R.

The digital baseband signal can be written as:

$\begin{matrix}{{s_{BB}^{\lbrack T\rbrack}(t)} = {\sum\limits_{k = 0}^{K - 1}\;{{\Pi_{T_{s}}\left( {t - t_{D}^{\lbrack T\rbrack} - {kT}_{s}} \right)}{s\lbrack k\rbrack}}}} & (2)\end{matrix}$where K is the number of samples of the waveform considered, Π_(T) _(s)is the gate function having width T_(s), t_(D) ^([T]) is the instantcorresponding to the beginning of the transmission or ToD (Time ofDeparture), measured with local clock of the transmitter, T_(s) is thesampling period and s[k] k=0, . . . ,K−1, are the samples of thewaveform, known a priori to the transmitter as well as the receiver. Forexample, the waveform may correspond to a synchronisation preamble of apacket, consisting of pilot symbols, or even to an entire packetassuming that demodulation is performed without error.

The baseband samples are then converted by a digital to analogueconverter (DAC). The DAC is not synchronised to the reference clock. Therelative time course of the local clock used for conversion with respectto the reference clock can be described by means of a frequency offset,δ_(f) ^([T]), and a time offset, t₀ ^([T]), that is:t ^([T])=(1+δ_(f) ^([T]))t+t ₀ ^([T])  (3)

The baseband signal is then translated to an intermediate frequencyf_(c), corresponding to the channel c, before being translated to the RFband. Alternatively, the signal can be directly translated to thefrequency F_(c) ^([T])=f_(RF)+f_(c) where f_(RF) is the frequency of theRF carrier.

In any case, the transmitted signal can be expressed in complex notationas:s _(c) ^([T])(t)=g _(c) ^([T]) s _(BB) ^([T])(t ^([T])) exp j(2πF _(c)^([T]) t+ϕc ^([T]))  (4)where F_(c) ^([T]) is the frequency of the transmitted signal, ϕc^([T])represents the phase of the original transmitted signal and g_(c) ^([T])is the complex gain of the transmitter. Both the frequency F_(c) ^([T])and the sampling rate f_(s)=1/T_(s) of the digital analogue converterare obtained from the local clock of the transmitter.

The signal transmitted by the connected object is received by thereceiver of a base station whose architecture has been schematicallyrepresented in FIG. 2 .

The receiver comprises a first stage, 210, known as the RF stage,providing translation of the RF signal received at an intermediatefrequency, and a second stage, 220, known as the IF stage, providestranslation to baseband.

The RF stage operates in analogue mode. It comprises a low noiseamplifier, 211, an RF mixer, 212, receiving a clock at the nominalfrequency f_(RF) generated by an RF oscillator, 213. In reality, thefrequency of the RF oscillator is shifted by one offset f_(RF)(1+δ_(f)^([R])), as will be seen later. The output signal from the mixer is thenfiltered by a low-pass filter, 214, before being sampled and convertedto digital by the analogue-to-digital converter, 215. Theanalogue-digital converter samples the signal at a sampling ratef_(s)=1/T_(s) obtained from a general synchronisation clock. This clockenables the base stations to be synchronised with each other, typicallywith an accuracy in the order of 10 to 30 ns in root mean square.

According to one advantageous characteristic of the invention, the IFstage operates in digital mode. The IF samples at the output of the ADC215 are translated into baseband by means of a complex multiplier, 216,receiving from a digital generator, 217, phasors in digital form.Specifically, these phasors, which represent complex valuesexp(−j2πf_(c)kT_(s)) operating at the channel frequency f_(c), areprovided to the complex multiplier, at the rate f_(s). The digitalgenerator 217 is controlled by a channel controller 218. On command fromthe controller 218, the digital generator 217 can vary the frequencyf_(c) by reading corresponding phasors from a memory (not shown). Thedigital generator is synchronised with the general synchronisationclock.

Advantageously, the overall synchronisation clock may be obtained byvirtue of a GNSS (Global Navigation Satellite System) receiver module,for example a GPS receiver code acquisition module. Alternatively, thegeneral synchronisation clock can be provided by the backhaul network ofa 5G network or fibre optic links between base stations. Alternatively,synchronisation can be obtained via the Internet using the Network TimeProtocol (NTP) from a time server. Other types of synchronisation withthe aforementioned precision may be contemplated.

When received by the base station, the RF signal is in the followingform, in which the additive noise component has been omitted:s _(c) ^([R])(t)=s _(c) ^([T])(t)*h ^([T,R])(t,τ)  (5)where h^([T,R])(t,τ) is the channel impulse response at instant tbetween the connected object and the base station under considerationand * is the convolution product. For simplicity of presentation andwithout loss of generality, it is assumed that this channel is timeinvariant. In practice, it will suffice if the channel is invariant forthe time of the measurement, that is essentially for the duration of thevirtual band scan. Furthermore, since the baseband signal is narrowband,the channel can be modelled, for each band around F_(c) ^([T]) by asimple complex coefficient, that is A_(c) ^([T,R]). The received signalcan then be written as:

$\begin{matrix}{\mspace{76mu}{{{s_{c}^{\lbrack R\rbrack}(t)} = {A_{c}^{\lbrack{T,R}\rbrack}{s_{c}^{\lbrack T\rbrack}\left( {t - \tau_{0}^{\lbrack{T,R}\rbrack}} \right)}}}\mspace{76mu}{with}}} & \left( {6\text{-}1} \right) \\{A_{c}^{\lbrack{T,R}\rbrack} = {{\alpha_{c}^{\lbrack{T,R}\rbrack}{\exp\left( {j\;\varphi_{c}^{\lbrack{T,R}\rbrack}} \right)}} = {\sum\limits_{p = 0}^{P - 1}\;{a_{p}^{\lbrack{T,R}\rbrack}{\exp\left( {{- j}\; 2\pi\;{F_{c}^{\lbrack T\rbrack}\left( {\tau_{p}^{\lbrack{T,R}\rbrack} - \tau_{0}^{\lbrack{T,R}\rbrack}} \right)}} \right)}}}}} & \left( {6\text{-}2} \right)\end{matrix}$where a_(p) ^([T,R]) and τ_(p) ^([T,R]) are respectively the attenuationcoefficients and delays of the different propagation paths, τ₀^([T,R])=d^([T,R])/c_(l) being the propagation time on the direct lineof sight (LOS) path where d^([T,R)] is the distance between theconnected object and the base station.

The received RF signal is frequency translated by mixing with thefrequency f_(RF) ^([R])=(1+δ_(f) ^([R]))f_(RF) where δ_(f) ^([R]) is therelative frequency offset between the transmitter and receiver. Thesignal at the intermediate frequency before analogue to digitalconversion can be represented in complex notation by:{tilde over (s)} _(c) ^([R])(t)=g _(c) ^([R]) s _(c) ^([R])(t)exp(−j(2πf _(RF) ^([R]) t+ϕ ^([R])))  (7)where g_(c) ^([R]) is the receiver gain at the frequency F_(c) ^([T])and ϕ^([R]) is the phase at the origin of the RF oscillator.

After sampling at the frequency f_(s)=1/T_(s), the samples of the signalat the

$\frac{{kT}_{s} - t_{0}^{\lbrack R\rbrack}}{1 + \delta_{f}^{\lbrack R\rbrack}}$

intermediate frequency are those taken at the times measured withrespect to the reference clock, that is:

$\begin{matrix}{{{\hat{s}}_{k}^{\lbrack R\rbrack}\left( {kT}_{s} \right)} = {{\overset{\sim}{s}}_{c}^{\lbrack R\rbrack}\left( \frac{{kT}_{s} - t_{0}^{\lbrack R\rbrack}}{1 + \delta_{f}^{\lbrack R\rbrack}} \right)}} & (8)\end{matrix}$as the receiver clock is not synchronised with the reference clock. Thetime relative to the local clock varies as t^(└R┘)=(1+δ_(f) ^(└R┘))t+t₀^(└R┘) where t₀ ^([R]) is a time offset and δ_(f) ^([R]) is the relativefrequency offset introduced earlier.

These samples are then translated into baseband by multiplication withthe digital phasors at the frequency of the channel under consideration:s _(BB,c)[R][k]=ŝk ^([R])(kT _(s))·exp(−j2πf _(c) kT _(s))+n _(c)^([T,R])[k]  (9)where exp(−j2πf_(c)kT_(s)), k=0, . . . , K−1, are the phasors inquestion and n_(c) ^([T,R])[k] are noise samples.

Combining expressions (2) to (4) and (6-1) to (9) gives the receivedsignal samples as a function of the baseband transmitted signal samples,that is:

$\begin{matrix}{{s_{{BB},c}^{\lbrack R\rbrack}\lbrack k\rbrack} = {{g^{\lbrack R\rbrack}g^{\lbrack T\rbrack}{\alpha_{c}^{\lbrack{T,R}\rbrack} \cdot \left\{ {\sum\limits_{\kappa = 0}^{K - 1}\;{{\Pi_{T_{s}}\left( {{\delta^{\lbrack{T,R}\rbrack}\left( {{kT}_{s} - t_{A}^{\lbrack{T,R}\rbrack}} \right)} - {\kappa\; T_{s}}} \right)}{s\lbrack\kappa\rbrack}}} \right\} \cdot \exp}\mspace{14mu}{j\left( {\phi_{c}^{\lbrack{T,R}\rbrack}\lbrack k\rbrack} \right)}} + {n_{v}^{\lbrack{T,R}\rbrack}\lbrack k\rbrack}}} & (10)\end{matrix}$with ϕc^([T,R])[k]=2πδ_(f) ^([T,R](f) _(RF)+f_(c))kT_(s)+ϕ_(A,c)^([T,R])[k].

The different terms appearing in expression (10) can be interpreted asfollows:

g_(c) ^([R]), g_(c) ^([T]) are the respective complex gains of thereceiver and transmitter at frequency F_(c). These gains generally varywith frequency and are estimated and compensated for in a priorcalibration phase.

α_(c) ^([T,R]) is the modulus of the complex coefficient of thetransmission channel at the frequency F_(c), its expression is given by:

$\begin{matrix}{\alpha_{c}^{\lbrack{T,R}\rbrack} = {{A_{c}^{\lbrack{T,R}\rbrack}} = {{\sum\limits_{p = 0}^{P - 1}\;{a_{p}^{\lbrack{T,R}\rbrack}{\exp\left( {{- j}\; 2{\pi\left( {\left( {{\left( {1 + \delta_{f}^{\lbrack T\rbrack}} \right)f_{RF}} + f_{c}} \right)\left( {\tau_{p}^{\lbrack{T,R}\rbrack} - \tau_{0}^{\lbrack{T,R}\rbrack}} \right)} \right)}} \right)}}}}}} & (11)\end{matrix}$

The attenuation coefficient α_(c) ^([T,R]) is constant within eachfrequency channel (flat fading) but varies from channel to channel dueto multiple paths of the transmission channel.

$\delta^{\lbrack{T,R}\rbrack} = \frac{1 + \delta_{f}^{\lbrack T\rbrack}}{1 + \delta_{f}^{\lbrack R\rbrack}}$is a time dilation factor between the transmitter and the receiver.

It reflects the shift in conversion (DAC) and sampling (ADC) timesbetween the transmitter and receiver.

$t_{A}^{\lbrack{T,R}\rbrack} = {{\left( {1 + \delta_{f}^{\lbrack R\rbrack}} \right)\tau_{0}^{\lbrack{T,R}\rbrack}} + {\frac{1 + \delta_{f}^{\lbrack R\rbrack}}{1 + \delta_{f}^{\lbrack T\rbrack}}\left( {t_{D}^{\lbrack T\rbrack} - t_{0}^{\lbrack T\rbrack}} \right)} + t_{0}^{\lbrack R\rbrack}}$is the time of arrival of the packet in the receiver time base. Thefirst term corresponds to the propagation time (affected by the drift ofthe receiver local clock with respect to the reference clock), thesecond term corresponds to the time of transmission of the packet(affected by the respective drifts of the transmitter and receiverclocks), and the last term corresponds to the time offset of thetransmitter.

$\delta_{f}^{\lbrack{T,R}\rbrack} = \frac{\delta_{f}^{\lbrack T\rbrack} - \delta_{f}^{\lbrack R\rbrack}}{1 + \delta_{f}^{\lbrack R\rbrack}}$reflects the relative clock frequency offset between the transmitter andthe receiver.

ϕ_(A,c) ^([T,R]) is the phase of arrival of the first sample of thepacket (k=0) arriving at the base station receiver:

$\begin{matrix}\begin{matrix}{\phi_{A,c}^{\lfloor{T,R}\rfloor} = {{{- 2}{\pi\left( {1 + \delta_{f}^{\lfloor T\rfloor}} \right)}\left( {f_{RF} + f_{c}} \right)\tau_{0}^{\lfloor{T,R}\rfloor}} + \varphi_{c}^{\lfloor{T,R}\rfloor}}} \\{{{+ 2}\pi f_{c}t_{0}^{\lbrack T\rbrack}} - {2{\pi\left( \frac{{\left( {\delta_{f}^{\lbrack T\rbrack} - \delta_{f}^{\lbrack R\rbrack}} \right)f_{RF}} + {\left( {1 + \delta_{f}^{\lbrack T\rbrack}} \right)f_{c}}}{1 + \delta_{f}^{\lceil R\rceil}} \right)}t_{0}^{\lbrack R\rbrack}}} \\{{+ \phi_{c}^{\lbrack T\rbrack}} - \phi^{\lbrack R\rbrack}}\end{matrix} & (12)\end{matrix}$and finally n_(c) ^([T,R])[k] is an assumed additive white Gaussiannoise (AWGN) sample.

The phase of arrival of the signal, that is the phase of a basebandsignal sample as it arrives at the receiver, is given by ϕ_(c)^([T,R])[k]=(2πδ_(f) ^([T,R])(f_(RF)+f_(c))kT_(s)+ϕ_(A,c) ^([T,R])[k]),as can be seen in equation (10).

Given expression (12), this phase of arrival is expressed as follows:

$\begin{matrix}\begin{matrix}{{\phi_{c}^{\lbrack{T,R}\rbrack}\lbrack k\rbrack} = {2{{\pi\delta}_{f}^{\lbrack{T,R}\rbrack}\left( {f_{RF} + f_{c}} \right)}{kT}_{s}}} \\{{{- 2}{\pi\left( {1 + \delta_{f}^{\lbrack T\rbrack}} \right)}\left( {f_{RF} + f_{c}} \right)\tau_{0}^{\lbrack{T,R}\rbrack}} + \varphi_{c}^{\lbrack{T,R}\rbrack}} \\{{{+ 2}\pi\; f_{c}t_{0}^{\lbrack T\rbrack}} - {2{\pi\left( \frac{{\left( {\delta_{f}^{\lbrack T\rbrack} - \delta_{f}^{\lbrack R\rbrack}} \right)f_{RF}} + {\left( {1 + \delta_{f}^{\lbrack T\rbrack}} \right)f_{c}}}{1 + \delta_{f}^{\lbrack R\rbrack}} \right)}t_{0}^{\lbrack R\rbrack}}} \\{{+ \phi_{c}^{\lceil T\rceil}} - \phi^{\lceil R\rceil}}\end{matrix} & (13)\end{matrix}$

Without loss of generality, the clock of the connected object can bearbitrarily taken as the reference clock, that is t₀ ^([T])=0, δ_(f)^([T]=)0 and

$\delta_{f}^{\lbrack{T,R}\rbrack} = {\frac{- \delta_{f}^{\lbrack R\rbrack}}{1 + \delta_{f}^{\lbrack R\rbrack}}.}$This reference is advantageous in that it lends itself well to theexpression of the phases of arrival of the base stations used to locatethe object. The phase of arrival of the signal is then expressed in asimpler way:

$\begin{matrix}\begin{matrix}{{\phi_{c}^{\lbrack{T,R}\rbrack}\lbrack k\rbrack} = {{- 2}\pi\frac{\delta_{f}^{\lbrack R\rbrack}}{1 + \delta_{f}^{\lceil R\rceil}}\left( {f_{RF} + f_{c}} \right){kT}_{s}}} \\{{{- 2}{\pi\left( {f_{RF} + f_{c}} \right)}\tau_{0}^{\lbrack{T,R}\rbrack}} + \varphi_{c}^{\lbrack{T,R}\rbrack}} \\{{- 2}{\pi\left( \frac{f_{c} - {\delta_{f}^{\lbrack R\rbrack}f_{RF}}}{1 + \delta_{f}^{\lbrack R\rbrack}} \right)}t_{0}^{\lbrack R\rbrack}} \\{{+ \phi_{c}^{\lceil T\rceil}} - \phi^{\lceil R\rceil}}\end{matrix} & (14)\end{matrix}$

When the signal transmitted by the connected node is received by aplurality of base stations, the difference in phase of arrival of thesignal received by the base station BS_(i) (equipped with the receiverR_(i)) and the base station BS_(l) (equipped with the receiver R_(l))enables the (unknown) phase ϕ_(c) ^([T]) of the RF signal to be removedfrom the transmitter:

$\begin{matrix}\begin{matrix}{{{\Delta\phi}_{c}^{\lbrack{R_{i},R_{\ell}}\rbrack}\lbrack k\rbrack} = {{{\phi_{c}^{\lbrack{T,R_{i}}\rbrack}\lbrack k\rbrack} - {\phi_{c}^{\lbrack{T,R_{\ell}}\rbrack}\lbrack k\rbrack}} = {{- 2}{\pi\left( {\frac{\delta_{f}^{\lbrack R_{i}\rbrack}}{1 + \delta_{f}^{\lbrack R_{i}\rbrack}} - \frac{\delta_{f}^{\lbrack R_{\ell}\rbrack}}{1 + \delta_{f}^{\lbrack R_{\ell}\rbrack}}} \right)}\left( {f_{RF} + f_{c}} \right){kT}_{s}}}} \\{{{- 2}{\pi\left( {f_{RF} + f_{c}} \right)}\left( {\tau_{0}^{\lbrack{T,R_{i}}\rbrack} - \tau_{0}^{\lbrack{T,R_{\ell}}\rbrack}} \right)} + \left( {\varphi_{c}^{\lbrack{T,R_{i}}\rbrack} - \varphi_{c}^{\lbrack{T,R_{\ell}}\rbrack}} \right)} \\{{+ 2}\pi\;{f_{RF}\left( {\frac{\delta_{f}^{\lbrack R_{i}\rbrack}t_{0}^{\lbrack R_{i}\rbrack}}{1 + \delta_{f}^{\lbrack R_{i}\rbrack}} - \frac{\delta_{f}^{\lbrack R_{\ell}\rbrack}t_{0}^{\lbrack R_{\ell}\rbrack}}{1 + \delta_{f}^{\lbrack R_{\ell}\rbrack}}} \right)}} \\{{- 2}\pi\;{f_{c}\left( {\frac{t_{0}^{\lbrack R_{i}\rbrack}}{1 + \delta_{f}^{\lbrack R_{i}\rbrack}} - \frac{t_{0}^{\lbrack R_{\ell}\rbrack}}{1 + \delta_{f}^{\lbrack R_{\ell}\rbrack}}} \right)}} \\{- \left( {\phi^{\lbrack R_{i}\rbrack} - \phi^{\lbrack R_{\ell}\rbrack}} \right)}\end{matrix} & (16)\end{matrix}$

The fact that the time difference of arrival no longer depends on thephase of the transmitter RF signal is essential, as it allows theconstraints on the transmitter hardware architecture, in particular onthe stability of its RF oscillator, to be completely dispensed with.

The phase difference of arrival between the two base stations comprisesseveral terms. The first term corresponds to the phase shift over timedue to the relative offset of the sampling frequencies in the receiversof the two base stations. The second term carries the useful informationof the difference in signal propagation time. The third term reflects asynchronisation error of the RF stages of the two receivers and thefourth term as a relative synchronisation error of the IF stages. Thesesynchronisation errors are due to the time offsets between the samplingfrequencies of the base stations. Finally, the last term is the phasedifference at the origin between the RF oscillators of the tworeceivers.

A key point to note is that, since the baseband translation is performeddigitally by phasors, no origin phase variation is introduced in the IFoscillator and therefore the last term remains constant during thevirtual band frequency scan. This feature especially avoids the need fora reference node having a known position, as required in prior art.

The locating principle by phase difference of arrival is based on theability to extract the propagation delay difference τ₀ ^([T,R) ^(i)^(])−τ₀ ^([T,R) ^(l) ^(]) (in LOS) from the slope of Δϕ_(c) ^(┌R) ^(i)^(,R) ^(l) ^(┐)[k], as a function of the channel frequency J. The firstand fourth terms of Δϕ_(c) ^(└R) ^(i) ^(,R) ^(l) ^(┘)[k], are spuriousterms that are also linearly dependent on frequency f_(c) and havetherefore be removed.

In practice, the phase shift Δϕ_(c) ^([R) ^(i) ^(,R) ^(l) ^(])[k], isnot calculated on each sample, but on each packet, an estimate of aphase of arrival averaged over the packet, called the packet phase ofarrival, for each base station, that is ϕ_(c) ^([T,R) ^(i) ^(]), ϕ_(c)^([T,R) ^(l) ^(]). This packet phase of arrival is obtained bycorrelating a packet of K samples with a pilot sequence (or with anerror-free decoded sequence). A packet phase difference of arrivalΔϕ_(c) ^([R) ^(i) ^(,R) ^(l) ^(])=ϕ_(c) ^([T,R) ^(l) ^(])−ϕ_(c) ^([T,R)^(l) ^(]) is derived for each channel.

The first term in (16) can be minimised by adopting the virtual bandfrequency scanning scheme disclosed in application DE-A-10 2007 043 649and illustrated in FIG. 3 . However, constraints inherent in thisscanning scheme can be relaxed as explained below.

The channel frequency has been represented on the ordinate and the timeon the abscissa. The virtual band B_(virt)=(C−1)Δf around the carrier isscanned in Δf hops, with a first scan in the uplink direction and asecond scan, temporally symmetrical to the first one, being performed inthe downlink direction. More specifically, the intermediate frequencyvaries in +Δf hops, so as to successively scan the channels C in theuplink direction on the first scan and then varied in −Δf hops so as tosuccessively scan the subsequent channels C in the downlink direction onthe second scan. It should be noted that the order of the scanningdirections is irrelevant. The transmitter transmits one sample packet Kat each frequency hop, that is the transmission period of time in eachchannel is KT_(s). Assuming that the intermediate frequency change isinstantaneous, the total scan period of time is 2CKT_(s).

The removal of the first term can be achieved by summing the packetphase differences of arrival, Δϕ_(c) ^([R) ^(i) ^(,R) ^(l) ^(]) andΔϕ_(2C+1−c) ^([R) ^(i) ^(,R) ^(l) ^(]) obtained for the same channelduring the uplink scan and downlink scan, the sum of the first terms of(16) then giving the phase error:

$\begin{matrix}{{- 4}{\pi\left( {\frac{\delta_{f}^{\lbrack R_{i}\rbrack}}{1 + \delta_{f}^{\lbrack R_{i}\rbrack}} - \frac{\delta_{f}^{\lbrack R_{\ell}\rbrack}}{1 + \delta_{f}^{\lbrack R_{\ell}\rbrack}}} \right)}\left( {f_{RF} + f_{c}} \right)CKT_{s}} & (17)\end{matrix}$

It is observed that the factor of (f_(RF)+f_(c)) no longer depends onthe packet rank. This observation is still true when programming of thechannel change is not instantaneous but lasts for a time θ, the periodof time CKT_(s) being simply increased by 2(C−1)θ.

Since this error component is a simple constant

${{- 4}{\pi\left( {\frac{\delta_{f}^{\lbrack R_{i}\rbrack}}{1 + \delta_{f}^{\lbrack R_{i}\rbrack}} - \frac{\delta_{f}^{\lbrack R_{\ell}\rbrack}}{1 + \delta_{f}^{\lbrack R_{\ell}\rbrack}}} \right)}{f_{RF} \cdot {CKT}_{s}}},$it is not taken into account in the extraction of the time difference ofarrival.

The phase error component due to the difference between thesynchronisation error of the IF stages linearly depends on f_(c).However, since F_(c)□f_(RF), the phase rotation due to

$\left( {\frac{\delta_{f}^{\lbrack R_{i}\rbrack}}{1 + \delta_{f}^{\lbrack R_{i}\rbrack}} - \frac{\delta_{f}^{\lbrack R_{\ell}\rbrack}}{1 + \delta_{f}^{\lbrack R_{\ell}\rbrack}}} \right)f_{c}$is relatively small. The sample rate offset of each receiver can beestimated in a conventional way by observing the phase time course ofthe received signal over several samples within the same channel. Thefrequency offsets thus estimated for the base station receivers BS_(i)et BS_(l) will be noted {circumflex over (δ)}_(f) ^([R) ^(i) ^(]) and{circumflex over (δ)}_(f) ^([R) ^(l) ^(]).

Once the period of time KT_(s) of a packet and, if necessary that, θ,separating two successive packets are known, the phase error (17) can beestimated.

In summary, if the scanning described above is performed and the packetphase differences of arrival are summed for channels of the samefrequency f_(2C+1−c)=f_(c), there is obtained, after removing the phaseerror introduced by the difference in the previously estimated frequencyoffsets:

$\begin{matrix}{{\phi_{c}^{\lbrack{R_{i},R_{\ell}}\rbrack} + \phi_{{2C} + 1 - c}^{\lbrack{R_{i},R_{\ell}}\rbrack} - \left\lbrack {{- 4}{\pi\left( {\frac{{\hat{\delta}}_{f}^{\lceil R_{i}\rceil}}{1 + {\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}} - \frac{{\hat{\delta}}_{f}^{\lceil R_{\ell}\rceil}}{1 + {\hat{\delta}}_{f}^{\lbrack R_{\ell}\rbrack}}} \right)}f_{c}CKT_{s}} \right\rbrack} = {{{- 4}{\pi\left( {f_{RF} + f_{c}} \right)}\left( {\tau_{0}^{\lbrack{T,R_{i}}\rbrack} - \tau_{0}^{\lbrack{T,R_{\ell}}\rbrack}} \right)} + \left( {\varphi_{c}^{\lbrack{T,R_{i}}\rbrack} - \varphi_{c}^{\lbrack{T,R_{\ell}}\rbrack}} \right) - {4\pi{f_{c}\left( {\frac{t_{0}^{\lbrack R_{i}\rbrack}}{1 + \delta_{f}^{\lbrack R_{i}\rbrack}} - \frac{t_{0}^{\lbrack R_{\ell}\rbrack}}{1 + \delta_{f}^{\lbrack R_{\ell}\rbrack}}} \right)}} + \Phi}} & (18)\end{matrix}$where Φ is a constant phase.

The sum of the packet phase differences for two symmetrical channels cand 2C+1−c is noted as Φ_(c) ^([R) ^(i) ^(,R) ^(l) ^(])=ϕ_(c) ^([R) ^(i)^(,R) ^(l) ^(])+ϕ_(2C+1−c) ^([R) ^(i) ^(,R) ^(l) ^(]) in the following.

It is important to note that the constraints on the frequency scan orderand scan uniformity can be relaxed. Indeed, it is understood that anypermutation (along the ordinate axis) of the frequencies f_(c)associated with the channel pairs c, 2C+1−c in FIG. 3 , can be performedwhile preserving the temporal symmetry, and thus the property expressedin (18). Moreover, it is not necessary to provide scan of the virtualband with a constant frequency hopping Δf, since the phase error givenby (17) can be corrected only by the knowledge of the frequency offsetsof the base stations and the value of the channel frequency f_(c)considered.

Knowing the transmitted sequence (for example a pilot sequence), eachbase station receiver can determine the modulus of the transfer functionof the transmission channel after baseband translation, in eachfrequency channel. Indeed, according to expression (10), the modulusα_(c) ^([T,R]) of the complex coefficient A_(c) ^([T,R]) of the transferfunction at the frequency f_(c) can be simply obtained by taking themodulus of the correlation of the sequence s_(BB,c) ^([R])[k], k=0, . .. , K−1 with the pilot sequence.

This gives the moduli α_(c) ^([T,R) ^(i) ^(])=α_(2C+1−c) ^([T,R) ^(i)^(]) for the base station BS_(i) and α_(c) ^([T,R) ^(l) ^(])=α_(2C+1−c)^([T,R) ^(l) ^(]) for the base station BS_(l).

The entity in charge of calculation then constructs a composite basebandtransfer function:{tilde over (H)} _(c) ^([R) ^(i) ^(,R) ^(l) ^(])α_(c) ^([T,R) ^(i)^(])=α_(2C+1−c) ^([T,R) ^(i) ^(])α_(c) ^([T,R) ^(l) ^(])=α_(2C+1−c)^([T,R) ^(l) ^(]) exp(jΦ _(c) ^([R) ^(l) ^(,R) ^(l) ^(]) ,c=1, . . .,C  (19)

This transfer function is none other than the product of two transferfunctions corresponding to the transmission channels between theconnected object and the two base stations respectively:{tilde over (H)} _(c) ^([R) ^(i) ^(,R) ^(l) ^(])=(H _(c) ^([T,R) ^(i)^(]))²((H _(c) ^([T,R) ^(l) ^(]))²)*  (20-1)where (H _(c) ^([T,R) ^(i) ^(]))²=α_(c) ^([T,R) ^(i) ^(])α_(2C+1−c)^([T,R) ^(i) ^(]) exp j(φ_(c) ^([T,R) ^(i) ^(])+φ_(2C+1−c) ^([T,R) ^(i)^(])), et(H _(c) ^([T,R) ^(l) ^(]))²=α_(c) ^([T,R) ^(l) ^(])α_(2C+1−c) ^([T,R)^(l) ^(]) exp j(φ_(c) ^([T,R) ^(l) ^(])+φ_(2C+1−c) ^([T,R) ^(l)^(])),  (20-2)

The transfer function (H_(c) ^([T,R) ^(i) ^(]))², c=1, . . . , C is noneother than the Fourier transform of the baseband impulse response,h^([T,R) ^(i) ^(]), of the channel between the connected object and thebase station, convolved with itself:{(H _(c) ^([T,R) ^(i) ^(]))² |c=1, . . . ,C}=DFT(h ^([T,R) ^(i)^(])(t)*h ^([T,R) ^(i) ^(])(t))  (21-1)Likewise:{(H _(c) ^([T,R) ^(l) ^(]))² |c=1, . . . ,C}=DFT(h ^([T,R) ^(l)^(])(t)*h ^([T,R) ^(l) ^(])(t))  (21-2)

The composite transfer function {tilde over (H)}_(c) ^([R) ^(i) ^(,R)^(l) ^(]) corresponds to a baseband impulse response:{tilde over (h)} _(c) ^(┌R) ^(i) ^(,R) ^(l) ^(┐)(t)=IDFT{{tilde over(H)} _(c) ^(┌R) ^(i) ^(,R) ^(l) ^(┐) |c=1, . . . ,C}=(h ^(┌T,R) ^(i)^(┐)(t)*^(┌T,R) ^(i) ^(┐)(t))⊗(h ^(┌T,R) ^(l) ^(┐)(t)*^(┌T,R) ^(l)^(┐)(t))  (22)where ⊗ is the correlation operator.

By virtue of its time reversal, convolution corrects the phase errorsdue to the frequency offsets of the RF oscillators in the two basestations. As for correlation, on the other hand, it enables the time oftransmission of the waveform to be dispensed with.

The peak of highest amplitude in the impulse response {tilde over(h)}^([R) ^(i) ^(,R) ^(l) ^(]) 0 allows the difference in propagationtime in line of sight between the connected object and the two basestations to be estimated:

$\begin{matrix}{{\tau_{0}^{\lbrack{T,R_{i}}\rbrack} - \tau_{0}^{\lbrack{T,R_{\ell}}\rbrack}} = {\frac{1}{2}\underset{t}{\arg\mspace{11mu}\max}\left( {{{\overset{\sim}{h}}^{\lbrack{R_{i},R_{\ell}}\rbrack}(t)}} \right)}} & (23)\end{matrix}$and, therefore, the distance difference Δd_(il), between the connectedobject and the two base stations BS_(i), BS_(l) is finally given by:

$\begin{matrix}{{\Delta d_{i\;\ell}} = {{c_{light}\left( {\tau_{0}^{\lfloor{T,R_{i}}\rfloor} - \tau_{0}^{\lfloor{T,R_{\ell}}\rfloor}} \right)} = {\frac{c_{light}}{2}\underset{t}{\arg\mspace{11mu}\max}\left( {{{\overset{\sim}{h}}^{\lbrack{R_{i},R_{\ell}}\rbrack}(t)}} \right)}}} & (24)\end{matrix}$

From the distance differences Δd_(il), and the positions of the basestations, the entity in charge of calculation can estimate by hyperbolictrilateration, the position of the connected object, in a way known perse.

The entity in charge of calculation can be a remote server or one of thebase stations participating in locating, which then plays the role ofreference base station.

FIG. 4 represents the flowchart of a method for locating a connectedobject in an LPWA network according to a first embodiment of the presentinvention.

For the sake of simplicity, only the steps performed by a base stationBS_(i) have been represented here. However, the skilled person willunderstand that similar steps are performed by the other base stationsparticipating in locating. As a general rule, locating a connectedobject requires a plurality (at least 3 in the case of a two-dimensionallocating) of base stations. The set of base stations participating inlocating will be noted Ω.

It is assumed that the object successively transmits signals (waveforms)at frequencies f_(RF)+f_(c), during packets (of duration KT_(s)), eachpacket corresponding to a transmission in a frequency channel f_(c). Thechannel frequency scans a predetermined virtual band a first time in afirst channel sequence and a second time in a second channel sequence,the first and second channel sequences being temporally symmetrical toeach other, with respect to an instant, t_(middle) (see FIG. 3 )corresponding to half of the full scan consisting of the first sequencefollowed by the second sequence. For example, the first channel sequenceis obtained by scanning in the uplink direction and the second channelsequence is obtained by scanning in the downlink direction.Advantageously, the uplink and downlink scans are performed uniformlywith a constant frequency hopping, Δf.

Steps 410-450 are performed in parallel by the base stations, and thensteps 460-490 are performed by the calculation server, based on theinformation transmitted by the latter. However, some of the steps420-440 entrusted to the base stations may be attributed to the server,provided that the necessary information is transmitted to it.

In step 410, the base station receiver BS_(i) translates the receivedsignal by mixing with the RF carrier frequency to obtain a channelsignal at an intermediate frequency, and then baseband translates thechannel signal, this baseband translation being performed digitally bymultiplication with phasors as described above.

In step 420, the receiver estimates, by means of a correlation with apilot sequence (or with a sequence of symbols received without error),the attenuation coefficient, α_(c) ^([T,R) ^(i) ^(]), of thetransmission channel, as well as the packet phase of arrival, Φ_(c)^([T,R) ^(i) ^(]), at the frequencies f_(RF)+f_(c) where f_(c), c=1, . .. , C are the frequencies of the different channels.

In step 430, the receiver performs the sum of the packet phases ofarrival for each pair of symmetrical channels, that is the sum relatesto packets at the same channel frequency but at opposite virtual bandscanning directions. This gives an averaged phase of arrival for eachchannel Φ_(c) ^([T,R) ^(i) ^(]).

If necessary, the scanning order of the different channel frequenciesmay be swapped and the hops between successive channel frequencies maynot be constant.

In step 440, the receiver BS_(i) makes an estimate of the frequencyoffset {circumflex over (δ)}_(f) ^([R) ^(i) ^(]) of its clock withrespect to that of the transmitter and corrects the phase arrival Φ_(c)^([T,R) ^(i) ^(]) of the phase error by adding

$4{\pi\left( \frac{{\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}}{1 + {\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}} \right)}f_{c}CKT_{s}$to it, for each of the frequency channels c=1, . . . , C:

$\Phi^{\prime_{\;_{c}}^{\lceil{T,R_{i}}\rceil}} = {\Phi_{c}^{\lceil{T,R_{i}}\rceil} + {4{\pi\left( \frac{{\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}}{1 + {\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}} \right)}f_{c}{{CKT}_{s}.}}}$

In step 450, the base station BS_(i) transmits the values {α_(c) ^([T,R)^(i) ^(]);Φ_(c) ^([T,R) ^(i) ^(])}, c=1, . . . , C to the calculationserver.

In step 460, the server calculates the phase differences of arrival foreach pair of the set of base stations, that is for the base stationsBS_(i) and BS_(l)Φ_(c) ^([R) ^(i) ^(,R) ^(l) ^(])=Φ′_(c) ^([T,R) ^(i)^(])−Φ′_(c) ^([T,R) ^(l) ^(]), for each channel c=1, . . . , C.

In step 470, the server constructs the composite baseband transferfunctions {tilde over (H)}_(c) ^([R) ^(i) ^(,R) ^(l) ^(])={{tilde over(H)}_(c) ^([R) ^(i) ^(,R) ^(l) ^(]); c=1, . . . , C} for each pair ofbase stations BS_(i), BS_(l) of Ω, by means of expression (19).

In step 475, the server performs an inverse Fourier transform (IDFT) ofeach of the composite transfer functions constructed in the previousstep, to generate the corresponding composite impulse responses, {tildeover (h)}^([R) ^(i) ^(,R) ^(l) ^(])(t) for each pair of base stationsBS_(i), BS_(l) of Ω.

When the order of the scanned frequencies has been swapped in any wayfrom that of a linear uplink or downlink scan, the order of thecomposite transfer functions {tilde over (H)}_(c) ^([R) ^(i) ^(,R) ^(l)^(])={{tilde over (H)}_(c) ^([R) ^(i) ^(,R) ^(l) ^(]); c=1, . . . , C}is swapped in the opposite direction before the inverse Fouriertransform is applied. Finally, when the virtual band scan is non-uniforma non-uniform inverse Fourier transform (NU-IDFT) is applied to thecomposite transfer functions, using the actually scanned frequencies.

In step 480, the server detects the peak of highest amplitude in eachimpulse response {tilde over (h)}_(c) ^([R) ^(i) ^(,R) ^(l) ^(]) andderives, from the expression (23), the line of sight propagation timedifference between the connected object and the base stations BS_(i),BS_(l) of Ω. This detection is repeated for each impulse response {tildeover (h)}_(c) ^([R) ^(i) ^(,R) ^(l) ^(]). The server derives thedistance differences, Δd_(il), between the connected object and the basestations BS_(i), BS_(l), for each pair of base stations BS_(i), BS_(l)of Ω.

In step 490, the server estimates the position of the connected objectby hyperbolic trilateration from the distance differences Δd_(il)estimated in the previous step.

FIG. 5 schematically represents a method for locating a connected objectaccording to a second embodiment of the invention.

In this second embodiment, the steps performed by the base stations,collectively designated by the block 500, are identical to those alreadydescribed in relation to FIG. 4 .

However, the calculation server does not perform either explicitcalculation of the phase differences of arrival or explicit constructionof the baseband composite transfer function.

The estimation of the position of the connected object is obtained hereby a neural network, 550, whose input layer receives the values {α_(c)^([T,R) ^(i) ^(]);Φ′_(c) ^([T,R) ^(i) ^(])}, c=1, . . . ,C, of each basestation BS_(i) of the set Ω, and whose output layer receives thecoordinates of the object.

The neural network is previously trained on labelled data, that is onsets of such values associated with known positions. This labelled datacan be the result of a real measurement run (for example by means of ageo-referenced connected object) or it can be the result of asimulation. During the training phase, the set of synaptic coefficientsis updated from the labelled data, using the stochastic gradientalgorithm.

According to an alternative of the second embodiment, the neural networkdoes not directly provide the position of the object but simply thedifferences in propagation time τ₀ ^([T,R) ^(i) ^(])−τ₀ ^([T,R) ^(l)^(]) or, equivalently, the distance differences Δd_(il) for thedifferent pairs of base stations of Ω. A hyperbolic trilaterationalgorithm is then used to estimate the position of the connected object,as in the first embodiment.

Those skilled in the art will understand that, regardless of theembodiment, locating the connected object here only requires sending twopackets (per frequency channel) to the base stations and no geolocatedreference node is required.

FIG. 6 allows the comparison on one example of the root mean squareerror of the estimated position as a function of the signal-to-noiseratio, for a locating method according to the present invention and alocating method using time differences of arrival, known from the stateof the art.

The signal transmitted by the connected object of the LPWA network is a10 kchips/s BPSK signal (B_(inst)=10 kHz) modulating a 32 chip-lengthGold sequence. This sequence is repeated on C=16 frequency channelsscanned according to the symmetrical scan pattern illustrated in FIG. 3. The frequency channels are spaced with a frequency hopping of 200 kHz,resulting in a virtual bandwidth B_(viri) of 3 MHz. Only two basestations were taken into account, the position error being measured herewith respect to the hyperbola passing through the point where the objectis actually situated. It was assumed that the base stations and theconnected object were assigned a carrier frequency offset (CFO) in theorder of ±2 10⁻⁶.

For a signal-to-noise ratio E_(s)/N₀ of 25 dB, the root mean squareerror of the position of the connected object, obtained by means of atrilateration method based on Time Differences of Arrival (TDoA), is 300m, whereas it is only 2 m by means of the Phase Difference of Arrival(PDoA) locating method according to the present invention.

FIG. 6 also shows the variation in the root mean square error of theposition of the object as a function of the synchronisation standarddeviation of the base station. For example, for a synchronisationstandard deviation in the order of 30 ns (case of a GNSS clock), theroot mean square error on the object position switches to 13 m which isstill much lower than the error obtained by TDoA.

The invention claimed is:
 1. A method for locating a connected object inan LPWA network using a plurality of base stations, the connected objecttransmitting an RF signal comprised of a sequence of packets in aplurality of frequency channels forming a virtual band, the virtual bandbeing scanned a first time according to a first channel sequence and asecond time according to a second channel sequence, the first and secondchannel sequences being temporally symmetrical to each other, wherein:(a) each base station performs translation of the RF signal at thechannel frequency, sampling of the RF signal translated, and thenbaseband translation in digital mode by multiplication with phasors, thesampling being synchronous with a general clock, common to all the basestations; (b) each base station estimates the attenuation coefficient ofthe transmission channel between the connected object and itself, inbaseband, as well as a phase of arrival of a packet, called a phase ofarrival, for each frequency channel of the first sequence and of thesecond sequence of channels; (c) each base station sums the phases ofarrival of packets relating to a same channel but to distinct sequencesof channels to obtain an averaged phase of arrival for each channel),(d) each base station estimates the frequency offset ({circumflex over(δ)}^([R) ^(i) ^(]) _(f)) between its sampling frequency and that of thetransmitter, and then corrects the averaged phase of arrival for eachchannel by a phase error due to this frequency offset, so as to obtainan averaged and corrected phase of arrival (Φ′^([T,R) ^(i) ^(]) _(c));(e) each base station transmits to a server the previously estimatedattenuation coefficients and averaged and corrected phases of arrival;(f) the server calculates, for each pair of base stations of saidplurality, the averaged and corrected phase differences of arrival so asto obtain phase differences of arrival ({Φ^([R) ^(i) ^(,R) ^(l) ^(])_(c)=Φ′^([T,R) ^(i) ^(]) _(c)−Φ′^([T,R) ^(l) ^(]) _(c)}), for eachchannel frequency; (g) the server constructs, for each pair (BS_(i),BS_(l)) consisting of a first and a second base station, a compositetransfer function ({tilde over (H)}^([R) ^(i) ^(,R) ^(l) ^(])) relatingto these two base stations, from the attenuation coefficients of thetransmission channel between the connected object and the first andsecond base stations respectively for the different frequency channels,as well as the phase differences of arrival obtained in the previousstep for the said pair of base stations and for these same frequencychannels; (h) the server performs an inverse Fourier transform of eachcomposite transfer function obtained in the previous step so as toobtain a composite impulse response ({tilde over (h)}^([R) ^(i) ^(,R)^(l) ^(])(t)) for each pair of base stations of said plurality; (i) theserver detects the peak of highest amplitude in each of the compositeimpulse responses and derives therefrom, for each pair (BS_(i),BS_(l))consisting of a first and a second base station, a distance difference(Δd_(il)) between the connected object and the first base station, onthe one hand, and between the connected object and the second basestation, on the other hand; (j) the server estimates the position of theconnected object by hyperbolic trilateration from the distancedifferences obtained in previous step (i).
 2. The method for locating aconnected object according to claim 1, wherein the first channelsequence is obtained by scanning in the uplink direction and the secondchannel sequence is obtained by scanning in the downlink direction, theuplink and downlink scans being performed uniformly with a constantfrequency hopping (Δf).
 3. The method for locating a connected objectaccording to claim 2, wherein in step (a), the baseband translation isperformed by multiplying, at the rate of the sampling frequency, thesamples of the translated RF signal, by phasors exp(−j2πf_(c)kT_(x))where f_(c) is the channel frequency, f_(x)=1/T_(x) is the samplingfrequency of the receiver and k is the rank of the sample.
 4. The methodfor locating a connected object according to claim 2, wherein in step(b) estimating the transmission channel coefficient and the phase ofarrival of a sample packet is achieved by correlating the sequence ofsamples of the baseband signal with a pilot sequence, the modulus of thecorrelation result being comprised of the gains of the transmitter andthe receiver to obtain said transmission channel coefficient.
 5. Themethod for locating a connected object according to claim 2, wherein instep (c) the base station performs, for each frequency channel, the sumΦ_(c) ^([T,R) ^(i) ^(])=ϕ_(c) ^([T,R) ^(i) ^(])+ϕ_(2C+1−c) ^([T,R) ^(i)^(]), ϕx[^(T,R) ^(i) ^(]) being the phase of arrival of the packet ctransmitted at the channel frequency f_(c) in a first scanning directionand ϕ_(2C+1−c) ^([T,R) ^(i) ^(]) is the phase of arrival of the packet2C+1−c transmitted at the channel frequency in a second scanningdirection opposite to the first one, K is the number of samples in apacket and C is the number of packets per scanning direction.
 6. Themethod for locating a connected object according to claim 2, wherein instep (d) the averaged phase of arrival Φ_(c) ^([T,R) ^(i) ^(]) iscorrected by$\Phi^{\prime_{\;_{c}}^{\lceil{T,R_{i}}\rceil}} = {\Phi_{c}^{\lceil{T,R_{i}}\rceil} + {4{\pi\left( \frac{{\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}}{1 + {\hat{\delta}}_{f}^{\lbrack R_{i}\rbrack}} \right)}f_{c}{CKT}_{s}}}$where δ_(f) ^([T,R) ^(i) ^(]) is the frequency offset estimated in thatsame step, f_(c) is the channel frequency, C is the number of packetsper scan, K is the number of samples per packet and f_(s)=1/T_(s) is thesampling frequency.
 7. The method for locating a connected objectaccording to claim 2, wherein in step (g), for each pair of basestations consisting of a first base station BS_(i) and a second basestation BS_(l), the server constructs the composite transfer function by{tilde over (H)}_(c) ^([R) ^(i) ^(,R) ^(l) ^(])=α_(c) ^([T,R) ^(i)^(])α_(2C+1−c) ^([T,R) ^(i) ^(])α_(c) ^([T,R) ^(l) ^(])α_(2C+1−c)^([T,R) ^(l) ^(]) exp(jΦ^([R) ^(i) ^(,R) ^(l) ^(])) where α_(c) ^([T,R)^(i) ^(]), α_(2C+1−c) ^([T,R) ^(i) ^(]) are the attenuation coefficientsof the transmission channel between the connected object and the basestation BS_(i) at the channel frequency f_(c), respectively in the firstand second scan, where α_(c) ^([T,R) ^(l) ^(]), α_(2C+1−c) ^([T,R) ^(l)^(]) are the attenuation coefficients of the transmission channelbetween the connected object and the base station BS_(i) at the channelfrequency f_(c), respectively in the first and second scan, and whereΦ_(c) ^([R) ^(i) ^(,R) ^(l) ^(]) is the phase difference of arrivalobtained in step (f) for the pair of base stations base BS_(i), BS_(l)and for the channel frequency f_(c).
 8. The method for locating aconnected object according to claim 2, wherein in step (i) the distancedifference between the connected object and a first base station BS_(i)on the one hand, and the connected object and a second base stationBS_(l) on the other hand, is obtained by${\Delta d_{i\;\ell}} = {\frac{c_{light}}{2}\underset{t}{\arg\mspace{11mu}\max}\left( {{{\overset{\sim}{h}}^{\lbrack{R_{i},R_{\ell}}\rbrack}(t)}} \right)}$where {tilde over (h)}^([R) ^(i) ^(,R) ^(l) ^(])(t) is the compositeimpulse response obtained in step (h) for the pair of base stationsBS_(i), BS_(l), and c_(light) is the speed of light.
 9. The method forlocating a connected object according to claim 1, wherein the overallclock is given by a GNSS reception module equipping each of the basestations of said plurality.
 10. The method for locating a connectedobject according to claim 1, wherein the overall clock is obtained viathe Internet by means of the NTP protocol from a time server.
 11. Themethod for locating a connected object according to claim 1, wherein theoverall clock is obtained via a backhaul network of a 5G network.
 12. Amethod for locating a connected object in an LPWA network using aplurality of base stations, the connected object transmitting an RFsignal comprised of a sequence of packets in a plurality of frequencychannels forming a virtual band, the virtual band being scanned a firsttime, according to a first channel sequence and a second time accordingto a second channel sequence, the first and second channel sequencesbeing temporally symmetrical to each other, wherein: (a) each basestation performs translation of the RF signal at the channel frequency,sampling of the RF signal translated, and then baseband translation indigital mode by multiplication with phasors, the sampling beingsynchronous with a general clock, common to all the base stations; (b)each base station estimates the attenuation coefficient of thetransmission channel between the connected object and itself, inbaseband, as well as a phase of arrival of a packet, called a phase ofarrival, for each frequency channel of the first sequence and of thesecond sequence of channels; (c) each base station sums the phases ofarrival of packets relating to a same channel but to distinct sequencesof channels to obtain an averaged phase of arrival for each channel(Φ_(c) ^([T,R) ^(i) ^(])); (d) each base station estimates the frequencyoffset ({circumflex over (δ)}_(f) ^([R) ^(i) ^(])) between its samplingfrequency and that of the transmitter, and then corrects the averagedphase of arrival for each channel by a phase error due to this frequencyoffset, so as to obtain an averaged and corrected phase of arrival(Φ′_(c) ^([T,R) ^(i) ^(])); (e) each base station transmits to a serverthe previously estimated attenuation coefficients and averaged andcorrected phases of arrival; (f) the server includes a previouslytrained neural network, the attenuation coefficients and the averagedand corrected phases of arrival for each base station of said pluralitybeing provided to the input layer of the neural network and the outputlayer of the neural network providing an estimate of the position of theconnected object.